Accuracy is the closeness of a measured value to the true value.

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Presentation on theme: "Accuracy is the closeness of a measured value to the true value."— Presentation transcript:

1 Accuracy is the closeness of a measured value to the true value. For example, the measured density of water has become more accurate with improved experimental design, technique, and equipment.Density of H2O at 20° C(g/cm3)11.01.000.9980.9982

2 ACCURACYPercent error is used to estimate the accuracy of a measurement.Percent error will always be a positive.What is the percent error if the measured density of titanium (Ti) is 4.45 g/cm3 and the accepted density of Ti is 4.50 g/cm3?

3 Measured ConcentrationPRECISIONPrecision is the agreement between repeated measurements of the same sample. Precision is usually expressed as a standard deviation.For example, the precision of a method for measuring arsenic (As) was determined by measuring 7 different solutions each containing 14.3 μg/L of As.Measured Concentration(μg/L)18.413.614.216.017.8Average = 15.3 μg/LStandard Deviation = 2.1 μg/LWhat is the true concentration of As in this experiment?Estimate the accuracy of this method.How precise is this method?14.3 μg/L2.1 μg/L

4 ACCURACY AND PRECISIONDescribe the accuracy and precision of these 4 targets.Accurate, and precisePrecise, but not accurateAccurate, but not preciseNot accurate, and not precise

5 ERRORSSystematic (or determinate) errors are reproducible and cause a bias in the same direction for each measurement.For example, a poorly trained operator that consistently makes the same mistake will cause systematic error. Systematic error can be corrected.Random (or indeterminate) errors are caused by the natural uncertainty that occurs with any measurement.Random errors obey the laws of probability. That is, random error might cause a value to be over predicted during its first measurement and under predicted during its second measurement. Random error cannot be corrected.

6 INTERPOLATION AND SIGNIFICANT FIGURESBy convention, a measurement is recorded by writing all exactly known numbers and 1 number which is uncertain, together with a unit label.All numbers written in this way, including the uncertain digit, are called significant figures.For example, the blue line is 2.73 cm long. This measurement has 3 significant figures. The first 2 digits (2.7 cm) are exactly known. The third digit (0.03 cm) is uncertain because it was interpolated or estimated 1 digit beyond the smallest graduation.

7 INTERPOLATION AND SIGNIFICANT FIGURESWhat is the volume of water in this graduated cylinder? Always measure the volume of a liquid at the bottom of the meniscus. The units are mL.The volume of water is 52.8 mL. The 52 mL are exactly known, and the 0.8 mL is uncertain because it was interpolated or estimated 1 digit beyond the smallest graduation.

11 SIGNIFICANT FIGURES, MULTIPLICATION, AND DIVISIONWhen multiplying or dividing the answer will have the same number of significant digits as the least accurate number used to get the answer. For example, …2.005 g / 4.95 mL = g/mLWhat is x 2.6?What is / 2.6?

12 SIGNIFICANT FIGURES AND CALCULATIONS THAT REQUIRE MULTIPLE STEPSAn average is the best estimate of the true value of a parameter.A standard deviation is a measure of precision.Averages and standard deviations require several steps to calculate. You must keep track of the number of significant figures during each step. Do NOT discard or round any figures until the final number is reported.